Problem: Rewrite as a simplified fraction. ${0.93\overline{8} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 938.8888...\\ 100x &= 93.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 845}$ ${x = \dfrac{845}{900}} $ ${x = \dfrac{169}{180}} $